Root locus design with CPISL compensation and the parallel inner loop form

Root locus design for integral control using the dominant second order poles technique often gives unsatisfactory results for two reasons. The first reason is that the zeros of the compensator cause the overshoot to be much larger than the overshoot of the model second order system with the desired poles. The second, more subtle problem is that poles at the origin moving along the negative real axis cannot move left past real axis zeros. These “blocked” poles often end up dominating the closed-loop response. This paper presents an easy to follow design procedure using the Complex Proportional-Integral-Lead (CPIL) compensator or Complex Proportional-Integral-Super-Lead (CPISL) compensator to address the “blocked” poles issue. The procedure also uses the parallel-inner loop form of implementing a controller with integral action to address the excess overshoot issue. We illustrate this design procedure for a double integrator plant.